If one really wants to understand the formulas for how to construct the Reshetikhin-Turaev 3-manifold invariants coming from quantum groups in terms of R-matrices and such, what's the best reference to read?

Edit: Apparently I'm being too vague. Let me explain my motivation a little bit. Right now, I'm thinking about how to categorify Chern-Simons theory. I understand most of the maps from quantum groups like the R-matrix quite well, so I would like a good reference that has formulae I can try to categorify based the bits I already understand.

Are you interested in the details of the R-matrix and other U_q(g) stuff, or are you more interested in combinatorial topology and handle-slide invariance? Or something else?
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Kevin WalkerOct 13 '09 at 19:54

I'm interested in general formulas that I actually understand each term of in terms of quantum groups. Though understandable stuff about combinatorial topology would be good too.
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Ben Webster♦Oct 13 '09 at 20:51

The formula is hard to implement but not difficult conceptually. The R-matrix formalism gives a link invariant for each irreducible representation. This is then extended to linear combinations of representations. For a 3-manifold invariant you take the regular representation. This means sum over irreducible representations the irreducible with scalar factor the quantum dimension. Then up to normalisation, this is a 3-manifold invariant by Kirby calculus.